Method of accurately determining similarity between target image and reference image

ABSTRACT

Provided is a method of determining a similarity between a target image and a reference image. The method includes (a) obtaining related approximation pixel-values of the reference image p t  having overall relationship between coordinates (x, y) and original pixel-values f t  of pixels of the reference image; (b) obtaining related approximation pixel-values of the target image p s  having overall relationship between coordinates (x, y) and original pixel-values f s  of pixels of the target image; and (c) determining the similarity using the target related approximation pixel-values p s  and the reference related approximation pixel-values p t .

BACKGROUND OF THE INVENTION

This application claims the priority of Korean Patent Application No.10-2005-0092159, filed on Sep. 30, 2005, in the Korean IntellectualProperty Office, the disclosure of which is incorporated herein in itsentirety by reference.

1. Field of the Invention

The present invention relates to a method of determining a similaritybetween a target image and a reference image, and more particularly, toa method of determining a similarity between a target image and areference image using a vision system included in a part mounter.

2. Description of the Related Art

A conventional part recognition method used by a part mounter isdisclosed in Japanese Patent Publication No. 2002- 222420 (title: ImageRecognition Method). In this conventional part recognition method,picked-up parts are recognized using geometrical information such aslead shapes or edge shapes of the picked-up parts.

Another conventional part recognition method is disclosed in JapanesePatent Publication No. 2003-256809 (title: Image Processing Apparatusand Method). In this conventional part recognition method, picked-upparts are recognized using brightness information thereof.

According to such conventional part recognition methods, a part mountercan recognize parts with characteristic shapes but cannot recognizeparts without characteristic shapes. FIG. 1 illustrates parts withcharacteristic shapes. FIG. 2 illustrates parts without characteristicshapes.

To recognize the parts without characteristic shapes as illustrated inFIG. 2, reference images, which are which are images of portions ofreference parts of each type, are stored. Then, whether an image of apicked-up part includes a reference image is determined. In so doing,the type of the picked-up part can be determined.

In other words, it is required to determine a similarity between atarget image, which is an image of part of a picked-up image, and areference image. Therefore, a method of accurately determining asimilarity between a target image and a reference image, even though theoriginal pixel-values of pixels of the target image minutely varyaccording to photographing and image-processing conditions, is required.

SUMMARY OF THE INVENTION

The present invention provides a method of accurately determining asimilarity between a target image and a reference image even thoughoriginal pixel-values of pixels of the target image minutely varyaccording to photographing and image-processing conditions. Therefore,parts without characteristic shapes can be accurately recognized.

In another embodiment of the present invention, there is provided amethod of determining a similarity between a target image and areference image, the method including: (a) obtaining relatedapproximation pixel-values of the reference image having overallrelationship between coordinates and original pixel-values f_(t) ofpixels of the reference image; (b) obtaining target relatedapproximation pixel-values having overall relationship betweencoordinates and original pixel-values of pixels of the target image; and(c) determining the similarity using the target related approximationpixel-values and the reference related approximation pixel-values.

As used herein, the term “original pixel-value” means a brightness valuethat is sensed from a pixel, and the term “related approximationpixel-value” means a value of a pixel that has relationship betweencoordinates (x,y) of the pixel and the “original pixel-value.”

In a similarity determination method according to the present invention,a similarity between a target image and a reference image is determinedusing target related approximation pixel-values p_(s), which haveoverall relationship, of the target image and the reference relatedapproximation pixel-values p_(t), which have overall relationship, ofthe reference image. Accordingly, although the original pixel-valuesf_(s) of pixels of the target image minutely vary according tophotographing and image-processing conditions, the similarity betweenthe target image and the reference image can be accurately determined.Consequently, parts without characteristic shapes can be accuratelyrecognized.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features and advantages of the present inventionwill become more apparent by describing in detail exemplary embodimentsthereof with reference to the attached drawings in which:

FIG. 1 illustrates parts with characteristic shapes;

FIG. 2 illustrates parts without characteristic shapes;

FIG. 3 is a block diagram of a part mounter using a similaritydetermination method according to an embodiment of the presentinvention;

FIG. 4 is a diagram for explaining a similarity determination methodaccording to an embodiment of the present invention;

FIG. 5 is a flowchart illustrating the similarity determination methodof FIG. 4;

FIG. 6 is a detailed flowchart illustrating one way of obtaining targetrelated approximation pixel-values in the method illustrated in FIG. 5;and

FIG. 7 is a flowchart illustrating an example in which a vision systemof the part mounter of FIG. 3 uses the similarity determination methodillustrated in FIG. 4.

DETAILED DESCRIPTION OF THE INVENTION

The present invention will now be described more fully with reference tothe accompanying drawings, in which exemplary embodiments of theinvention are shown. The invention may, however, be embodied in manydifferent forms and should not be construed as being limited to theembodiments set forth therein; rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the concept of the invention to those skilled in the art.

FIG. 3 is a block diagram of a part mounter using a similaritydetermination method according to an embodiment of the presentinvention. Referring to FIG. 3, the part mounter includes a drivingsystem DS, a line scan camera C, a vision system VS, and a maincontroller MC.

When in operation, the driving system DS drives a part-mounting head H.The line scan camera C takes a photograph of a target part P beingmoved, for example, an integrated circuit device absorbed to a nozzle ofthe part-mounting head H. The vision system VS processes image datareceived from the line scan camera C and generates position informationof a target part PT_(f). In this case, the vision system VS firstdetermines the type of the target part PT_(f) using the similaritydetermination method according to an embodiment of the presentinvention, which will be described later with reference to FIGS. 4through 6.

The main controller MC controls the driving system DS based on positioninformation received from the vision system VS. The nozzle N is adheredto the part-mounting head H of the part mounter. The target part PT_(f),for example, an integrated circuit device, is mounted on the nozzle Ndue to a pressure change within the nozzle N. Here, the line scan cameraC is located on a common path of the part-mounting head H. The line scancamera C takes a photograph of the target part PT_(f) absorbed to thenozzle N and outputs data. In other words, as the target part PT_(f)passes the line scan camera C, the line scan camera C captures andoutputs image data of continuous lines. The image data output from theline scan camera C is provided to the vision system VS included in thepart mounter, and an image frame is captured within the vision systemVS. Here, an illuminator I coupled to the line scan camera C may includea plurality of light sources, for example, three light emitting diodes,arranged to provide uniform intensity of illumination to all imagingregions of the line scan camera C.

FIG. 4 is a diagram for explaining a similarity determination methodaccording to an embodiment of the present invention. FIG. 5 is aflowchart illustrating the similarity determination method of FIG. 4.FIG. 6 is a detailed flowchart illustrating operation (b) of FIG. 5.

As described above, to recognize a target part PT_(f) without acharacteristic shape, it is required to store a reference image 399,which is an image of a portion of a reference part PT_(t), and an imageof the picked-up target part PT_(f) is analyzed to determine whether itincludes the reference image 399. In this case, a plurality of targetimages 201 through 299 that are of equal size compared to that of thereference image 399 exist in the image of the target part PT_(f).Referring to FIG. 4, as a result of sequentially comparing the targetimages 201 through 299 with the reference image 399, the target image299 is determined to be identical to the reference image 399. A methodof determining a similarity between any one of the target images 201through 299 and the reference image 399 will now be described withreference to FIGS. 4 through 6.

In operation (a), related approximation pixel-values of the referenceimage 399 p_(t) having overall relationship between coordinates (x, y)and original pixel-values f_(t) of pixels of the reference image 399 areobtained.

In operation (b), target related approximation pixel-values p_(s) havingoverall relationship between coordinates (x, y) and originalpixel-values f_(s) of pixels of a target image (any one of the targetimages 201 through 299) are obtained. An algorithm for performingoperation (a) on the reference image 399 is identical to an algorithmfor performing operation (b) on the target image (any one of the targetimages 201 through 299). Hence, only the algorithm for performingoperation (b) will now be described.

A polynomial equation having variables and unknown constantscorresponding to coordinates (x, y) of pixels of a target image (any oneof the target images 201 through 299 is set (operation b1). Morespecifically, the unknown constants are a₁₀, a₀₁, a₂₀ and a₀₂, and aquadratic polynomial equation thereof is set by Equation 1.p _(s) =a ₀₀ +a ₁₀ x+a ₀₁ y+a ₂₀ x+a ₁₁ xy+a ₀₂ y ²   (1)where p_(s) indicates target related approximation pixel-values whichwill be obtained as a result of Equation 1.

The unknown constants of the quadratic polynomial equation may beexpressed as a matrix A_(s) as given by Equation 2 $\begin{matrix}{A_{s} = {\begin{bmatrix}a_{00} \\a_{10} \\a_{01} \\a_{20} \\a_{11} \\a_{02}\end{bmatrix}.}} & (2)\end{matrix}$

In addition, coordinate variables of the quadratic polynomial equationcan be expressed as a coordinate matrix X as given by Equation 3$\begin{matrix}{X = {\begin{bmatrix}1 \\x \\y \\x^{2} \\{xy} \\y^{2}\end{bmatrix}.}} & (3)\end{matrix}$

Therefore, assuming that a transposed matrix of the matrix A_(s) isA_(s)′, the quadratic polynomial equation of Equation 1 may be convertedinto a determinant as given by Equation 4p_(s)=A_(s)′X   (4).

The unknown constants As of the polynomial equation are obtained under acondition that can minimize the differences between the originalpixel-values f_(s) of the pixels of the target image (any one of thetarget images 201 through 299) and the target related approximationpixel-values p_(s) to be obtained as a result of Equation 4, therebycompleting the polynomial equation (operation b2).

More specifically, a value Xf_(s) is obtained for each of the pixels ofthe target image by multiplying the coordinate matrix X of Equation 3 bythe original pixel-values f_(s). In this case, a sum ΣXf_(s) of thevalues Xf_(s) is a sensed concentrative moment U_(sf) of the targetimage, which satisfies Equation 5.U_(sf)=ΣXf_(s)   (5).

Next, the unknown constants A_(s) of the quadratic polynomial equationare obtained under a condition that can minimize a sum E_(s) of squares(p_(s)−f_(s))² of the differences between the original pixel-valuesf_(s) of the pixels of the target image and the target relatedapproximation pixel-values p_(s) to be obtained as a result of Equation4.

Here, a deviation E_(s), which is a sum of the squares (p_(s)−f_(s))²,may be defined by Equation 6 $\begin{matrix}{E_{s} = {\sum{\left( {p_{s} - f_{s}} \right)^{2}.}}} & (6)\end{matrix}$

When Equation 4 is substituted for Equation 6, Equation 7 can beobtained. $\begin{matrix}{E_{s} = {\sum{\left( {{A_{s}^{\prime}X} - f_{s}} \right)^{2}.}}} & (7)\end{matrix}$

A sum-matrix ∑XX^(′),which is a sum of the result of multiplying the coordinate matrix X ofthe Equation 3 with a transposed matrix X′ of the matrix X, may bedefined by Equation 8 $\begin{matrix}{{\sum{XX}^{\prime}} = {\begin{bmatrix}1 & x & y & x^{2} & {xy} & y^{2} \\x & x^{2} & {xy} & x^{3} & {x^{2}y} & {xy}^{2} \\y & {xy} & y^{2} & {x^{2}y} & {xy}^{2} & y^{3} \\x^{2} & x^{3} & {x^{2}y} & x^{4} & {x^{3}y} & {x^{2}y^{2}} \\{xy} & {x^{2}y} & {xy}^{2} & {x^{3}y} & {x^{2}y^{2}} & {xy}^{3} \\y^{2} & {xy}^{2} & y^{3} & {x^{2}y^{2}} & {xy}^{3} & y^{4}\end{bmatrix}.}} & (8)\end{matrix}$

When Equations 5 and 8 are substituted for Equation 7, Equation 7 isconverted into Equation 9. $\begin{matrix}{E_{s} = {{{A_{s}^{\prime}\left( {\sum{XX}^{\prime}} \right)}A_{s}} - {2A_{s}^{\prime}U_{sf}} + {f_{s}^{2}.}}} & (9)\end{matrix}$

Assuming that the coordinate-multiplication matrix XX′ is replaced withB, Equation 9 is converted into Equation 10. $\begin{matrix}{E_{s} = {{A_{s}^{\prime}{BA}_{s}} - {2A_{s}^{\prime}U_{sf}} + {\sum{f_{s}^{2}.}}}} & (10)\end{matrix}$

Therefore, an equation, which can minimize the differences E_(s) betweenthe original pixel-values f_(s) of the pixels of the target image (anyone of the target images 201 through 299) and the target relatedapproximation pixel-values p_(s) obtained as a result of Equation 4, isEquation 11. $\begin{matrix}{\frac{\partial E_{s}}{\partial A_{s}} = 0.} & (11)\end{matrix}$

When Equation 11 is solved assuming that an inverse matrix of thecoordinate-multiplication coordinate B is B⁻¹, the unknown constantsA_(s) of the polynomial equation are calculated usingA _(s′) =B ⁻¹ U _(sf)   (12).

Therefore, when Equation 12 is substituted for Equation 4, Equation 13used to calculate the target related approximation pixel-values p_(s) isobtained.p _(s) =U′ _(sf) B ⁻¹ X   (13)where U′_(sf) indicates a transposed matrix of the perceivedconcentrative moment U_(sf).

Then, values of the coordinates (x, y) are respectively substituted forthe complete polynomial equation of Equation 13 to obtain the targetrelated approximation pixel-values p_(s) (operation b3).

As described above, Equation 13 used to obtain the target relatedapproximation pixel-values p_(s) can also be used to obtain thereference related approximation pixel-values p_(t) of the referenceimage 399. In other words, the reference related approximationpixel-values p_(t) which has overall relationship, of the referenceimage 399 can be calculated usingp _(t) =U′ _(tf) B ⁻¹ X   (14)where U′_(tf) indicates a transposed matrix of the perceivedconcentrative moment U_(tf) of the reference image 399.

Next, in operation (c), a similarity is determined using the targetrelated approximation pixel-values p_(s) and the reference relatedapproximation pixel-values p_(t). In other words, the similarity isdetermined using the reference related approximation pixel-values p_(s),which have overall relationship, of the target image and the referencerelated approximation pixel-values p_(t), which have overallrelationship, of the reference image 399. Accordingly, although theoriginal pixel-values f_(s) of the pixels of the target image minutelyvary according to photographing and image-processing conditions, thesimilarity between the target image and the reference image 399 can beaccurately determined. Consequently, parts without characteristic shapescan be accurately recognized.

A conventional image similarity equation is defined by Equation 15$\begin{matrix}{h_{f} = \frac{\sum\limits_{x,y}{{f_{s}\left( {x,y} \right)}{f_{t}\left( {x,y} \right)}}}{\sqrt{\sum\limits_{x,y}{f_{s}^{2}\left( {x,y} \right)}}}} & (15)\end{matrix}$where h_(f) indicates a similarity between a target image and areference image, f_(s) indicates the original pixel-values of the targetimage, and f_(t) indicates the original pixel-values of the referenceimage.

To apply Equation 15 to the present invention, the original pixel-valuesf_(s) of the target image are replaced with the related approximationpixel-values p_(s) of the target image and the original pixel-valuesf_(t) of the reference image 399 are replaced with the relatedapproximation pixel-values p_(t) of the reference image 399 p_(t). Then,the similarity h_(p) between the target image (any one of the targetimages 201 through 299) and the reference image 399 can be obtainedusing $\begin{matrix}{h_{p} = {\frac{\sum\limits_{x,y}{{p_{s}\left( {x,y} \right)}{p_{t}\left( {x,y} \right)}}}{\sqrt{\sum\limits_{x,y}{p_{s}^{2}\left( {x,y} \right)}}}.}} & (16)\end{matrix}$

A process of simplifying Equation 16 into a determinant will bedescribed below. When Equation 16 is transformed as sum-matrix symbols,Equation 17 can be obtained. $\begin{matrix}{h_{p} = \frac{\sum{p_{s}p_{t}}}{\sqrt{\sum p_{s}^{2}}}} & (17)\end{matrix}$

When Equation 13 is substituted for Equation 17, Equation 18 below canbe obtained. $\begin{matrix}{h_{p} = \frac{\sum{U_{sp}^{\prime}B^{- 1}{Xp}_{t}}}{\sqrt{\sum p_{s}^{2}}}} & (18)\end{matrix}$where U′_(sp) indicates a transposed matrix of a connectionconcentrative moment U_(sp) of the target image. In this case, Equation18 is identical to $\begin{matrix}{h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}{\sum{Xp}_{t}}}{\sqrt{\sum p_{s}^{2}}}.}} & (19)\end{matrix}$

It can be understood from Equation 5 that ∑Xp_(t)in Equation 19 is a connection concentrative moment U_(tp) of thereference image 399. In other words, Equation 19 is identical to$\begin{matrix}{h_{p} = \frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{\sum p_{s}^{2}}}} & (20)\end{matrix}$

When the sensed concentrative moment U_(sf) of the target image isreplaced with the connection concentrative moment U_(sp) of the targetimage in Equation 13, the target related approximation pixel-valuesp_(s) is given by Equation 20p _(s) =U′ _(sp) B ⁻¹ X   (21).

When Equation 21 is substituted for Equation 20, Equation 22 can beobtained. $\begin{matrix}{h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{\sum\left( {U_{sp}^{\prime}B^{- 1}X} \right)^{2}}}.}} & (22)\end{matrix}$

Also, Equation 22 is identical to Equation 23 $\begin{matrix}{h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{\left( {\sum{U_{sp}^{\prime}B^{- 1}X}} \right)\left( {\sum{X^{\prime}B^{- 1}U_{sp}^{\prime}}} \right)}}.}} & (23)\end{matrix}$

Equation 23 is identical to Equation 24 $\begin{matrix}{h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{\sum{U_{sp}^{\prime}B^{- 1}{XX}^{\prime}B^{- 1}U_{sp}^{\prime}}}}.}} & (24)\end{matrix}$

Equation 24 is identical to Equation 25 $\begin{matrix}{h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{U_{sp}^{\prime}{B^{- 1}\left( {\sum{XX}^{\prime}} \right)}B^{- 1}U_{sp}^{\prime}}}.}} & (25)\end{matrix}$

Since the coordinate-multiplication matrix XX′ is B, Equation 25 isidentical to Equation 26 $\begin{matrix}{h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{\left( {U_{sp}^{\prime}B^{- 1}{BB}^{- 1}U_{sp}^{\prime}} \right)}}.}} & (26)\end{matrix}$

In conclusion, in operation (c), assuming that a transposed matrix ofthe connection concentrative moment U_(sp) of the target image isU′_(sp) and a connection concentrative moment of the target image isU_(tp), the similarity h_(p) is given by Equation 27 $\begin{matrix}{h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{U_{sp}^{\prime}B^{- 1}U_{sp}}}.}} & (27)\end{matrix}$

FIG. 7 is a flowchart illustrating an example in which the vision systemof the part mounter of FIG. 3 uses the similarity determination methodillustrated in FIGS. 4-6. A method of determining the type of apicked-up part PT_(f) using the vision system VS will now be describedwith reference to FIGS. 3, 4 and 7.

When the main controller MC generates a pick-up termination signal(operation 501), the vision system VS drives the line scan camera C andthus receives image data of the part PT_(f) from the line scan camera C(operation 502).

Next, the vision system VS sets a number n of a target image, which willbe sequentially applied, in the received image to “1” (operation 503).

Then, the vision system VS sets a number m of preset part type to “1”(operation 504).

The vision system VS calculates a similarity h (h_(p) in Equation 27,hereinafter indicated by h) between an n^(th) target image and areference image of an m^(th) type part using Equation 27 (operation505).

If the calculation result shows that the similarity h is greater than areference similarity href (operation 506), the vision system VS outputsinformation indicating that the currently picked-up part is the m^(th)type part (operation 507).

Conversely, if the calculation result shows that the similarity h isless than the reference similarity href (operation 506), the visionsystem VS performs the following operations.

If the current part type number m is not a final part type numberm^(fin) (operation 508), the vision system VS increases the number m ofthe current part type by one (operation 509) and performs operation 505and its subsequent operations.

If the current part type number m is the final part type number m_(fin)(operation 508), the current target image does not correspond to anypart type. Therefore, the vision system determines whether the currenttarget image number n is a final target image number n_(fin) (operation510).

If the vision system VS determines in operation 510 that the currenttarget image number n is not the final target image number n_(fin), itincreases the current target image number n by one (operation 511) andperforms operation 504 and its subsequent operations.

If the vision system VS determines in operation 510 that the currenttarget image number n is the final target image number n_(fin), it meansthe currently picked-up part PT_(f) does not correspond to any parttype. Therefore, the vision system VS outputs related error information(operation 512).

The above operations are repeated until an external termination signalis generated (operation 513).

As described above, in a similarity determination method according tothe present invention, a similarity between a target image and areference image is determined using target related approximationpixel-values p_(s), which have overall relationship, of the target imageand the reference related approximation pixel-values p_(t), which haveoverall relationship, of the reference image. Accordingly, although theoriginal pixel-values f_(s) of pixels of the target image minutely varyaccording to photographing and image-processing conditions, thesimilarity between the target image and the reference image can beaccurately determined. Consequently, parts without characteristic shapescan be accurately recognized.

While the present invention has been particularly shown and describedwith reference to exemplary embodiments thereof, it will be understoodby those of ordinary skill in the art that various changes in form anddetails may be made therein without departing from the spirit and scopeof the present invention as defined by the following claims.

1. A method of determining a similarity between a target image and areference image, the method comprising: (a) obtaining relatedapproximation pixel-values of the reference image, wherein the relatedapproximation pixel-values have an overall relationship betweencoordinates and original pixel-values f_(t) of pixels of the referenceimage; (b) obtaining target related approximation pixel-values havingoverall relationship between coordinates and original pixel-values ofpixels of the target image; and (c) determining the similarity using thetarget related approximation pixel-values and the reference relatedapproximation pixel-values.
 2. The method of claim 1, wherein algorithmsfor performing operations (a) and (b) are identical.
 3. The method ofclaim 2, wherein operation (b) comprises: (b1) setting a polynomialequation having variables and unknown constants corresponding to thecoordinates (x, y) of the pixels of the target image; (b2) completingthe polynomial equation by obtaining the unknown constants of thepolynomial equation under a condition that can minimize differencesbetween the original pixel-values f_(s) of the pixels of the targetimage and target related approximation pixel-values p_(s) to be obtainedas a result of the polynomial equation; and (b3) obtaining the targetrelated approximation pixel-values p_(s) by respectively substitutingvalues of the coordinates (x, y) for the polynomial equation completedin operation (b2).
 4. The method of claim 3, wherein, in operation (b1),the unknown constants are a₁₀, a₀₁, a₂₀ and a₀₂, and a quadraticpolynomial equationp _(s) =a ₀₀ +a ₁₀ x+a ₀₁ y+a ₂₀ x ² +a ₁₁ xy+a ₀₂ y ² is set
 5. Themethod of claim 4, wherein, in operation (b1), assuming that a matrixA_(s) of the unknown constants of the quadratic polynomial equation is${A_{s} = \begin{bmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}a_{00} \\a_{10}\end{matrix} \\a_{01}\end{matrix} \\a_{20}\end{matrix} \\a_{11}\end{matrix} \\a_{02}\end{bmatrix}},$ a transposed matrix of the matrix A_(s) is A_(s)′, anda coordinate matrix X is Y ${X = \begin{bmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}1 \\x\end{matrix} \\y\end{matrix} \\x^{2}\end{matrix} \\{x\quad y}\end{matrix} \\y^{2}\end{bmatrix}},$ the quadratic polynomial equation is converted into adeterminant by p_(s)=A_(s)′X.
 6. The method of claim 5, wherein, inoperation (b2), the unknown constants As of the quadratic polynomialequation-are obtained under a condition that can minimize a sum E_(s) ofsquares (p_(s)−f_(s))² of the differences between the originalpixel-values f_(s) of the pixels of the target image and the targetrelated approximation pixel-values p_(s) obtained as a result ofp_(s)=A_(s)′X.
 7. The method of claim 6, wherein, in operation (b2),assuming that a value Xf_(s) is obtained for each of the pixels of thetarget image by multiplying the coordinate matrix X by the originalpixel-values f_(s), that a sum ΣXf_(s) of the values Xf_(s) is a sensedconcentrative moment U_(sf) of the target image, that acoordinate-multiplication matrix obtained after the coordinate matrix Xis multiplied by a transposed matrix X′ is XX′, and that an inversematrix of the coordinate-multiplication coordinate XX′ is B⁻¹, theunknown constants A_(s) of the polynomial equation are calculated usingA_(s)=B⁻¹U_(sf).
 8. The method of claim 7, wherein, in operation (c),assuming that a transposed matrix of a connection concentrative momentU_(sp) of the target image is U′_(sp) and that a connectionconcentrative moment of the target image is U_(tp), the similarity h_(p)is given by$h_{p} = {\frac{U_{sp}^{\prime}B^{- 1}U_{tp}}{\sqrt{U_{sp}^{\prime}B^{- 1}U_{sp}}}.}$9. A method of determining a similarity between a target image, which isan image of portion of a picked up part, and a reference image using avision system included in a part mounter, the method comprising: (a)obtaining related approximation pixel-values of the reference imagehaving overall relationship between coordinates and originalpixel-values of pixels of the reference image; (b) obtaining targetrelated approximation pixel-values having overall relationship betweencoordinates and perceived luminacnes of pixels of the target image; and(c) determining the similarity using the target related approximationpixel-values and the reference related approximation pixel-values.
 10. Apart mounter, the part mounter comprising: a part-mounting head; anozzle coupled to the part-mounting head; a camera arranged across fromthe nozzle; a vision system coupled to the camera; a main controllercoupled to a driving system and the vision system, wherein the maincontroller controls the driving system based upon position informationreceived from the vision system; and wherein the vision systemphotographs a target part, thereby obtaining a target image, anddetermines a target part type by: (a) obtaining reference relatedapproximation pixel-values of a reference image having an overallconnection between coordinates and original pixel values of thereference image; (b) obtaining target related approximation pixel-valueshaving overall connection between coordinates and original pixel valuesof pixels of the target image; and (c) determining a similarity betweenthe target image and the reference image using the target relatedapproximation pixel values and the original pixel values.
 11. The partmounter of claim 10, further comprising an illuminator coupled to thecamera, wherein the illuminator comprises a plurality of light sources.